A Practical Recipe for Solving Difficult Epicyclic Gearbox Trains

Abstract

For a complete identification of a damaged element of an epicyclic gearbox (EG), it is necessary to calculate a list of characteristic frequencies, namely: total ratio, speed of rotating elements (possible ring, carrier or sun), gear meshing frequency (GMF), planet pass frequency (PPF), and the relative speed of a planet’s shaft, which is used for calculation of planets’ bearing characteristic frequencies. In case of a common one-stage epicyclic gearbox with stationary ring, i.e. so-called “planetary” gearbox, a complete list of formulas might be very easily found, e.g. on Wikipedia. However, these equations are just a simplified case of general formulas, where some parts of so-called “governing equations” have been assumed to zero and neglected. The current paper shows how to deal with a difficult, multi-stage epicyclic gearbox, which includes stages with all elements rotating, and where the phase marker is on the side of the gearbox with two unknown speeds requiring a construction of set of equations. Additionally, the paper illustrates common pitfalls when calculating characteristic frequencies of EG with modified teeth, i.e. where the commonly assumed equity of number of teeth of the ring gear versus sum of number of teeth on the sun gear and twice the number of teeth on the planet gear (ZR = ZS + 2 * ZP) is not fulfilled.